This article is cited in 7 papers

A numerical method for solving systems of nonlinear equations

A. A. Abramov^ab, L. F. Yukhno<sup>cd

a</sup> Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
^b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
^c Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
^d National Research Nuclear University, Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: Under certain conditions on nonlinear equations in a real finite-dimensional space, a numerical method for solving such equations is proposed. The method is based on the use of an auxiliary differential equation. A fairly rough approximate solution to this equation can be refined by applying Newton's method to the original problem. The result produced by the auxiliary equation is automatically a good initial approximation for Newton’s method. This combination ensures that the original problem can be solved to the required accuracy starting from any initial approximation.

Key words: system of nonlinear equations, Newton's method, Hadamard existence theorem.

UDC: 519.624

MSC: 65H10

Received: 21.04.2015

DOI: 10.7868/S0044466915110022

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:11, 1794–1801

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